CP Asymmetries and Higher-Order Unitarity Relations

Abstract

The main focus of this paper is to introduce a new method to control perturbative calculations of CP asymmetric reaction rates in the Boltzmann equation. CP asymmetries in particle reactions are traditionally calculated in terms of complex couplings, Feynman integrals, and Cutkosky rules. We use an expansion of the $S$-matrix unitarity condition instead, obtaining a general expression for the asymmetries without reference to the imaginary part of the loops. Asymmetry cancelations implied by CPT and unitarity are manifested in a diagrammatic way and easy to track at any order of perturbation theory. We demonstrate the power of this general framework within the right-handed neutrino and top-quark scattering asymmetries in seesaw type-I leptogenesis.

7 pages, 3 figures

References in corpus (5)

• Asymmetric Dark Matter
• Flavour Matters in Leptogenesis
• Asymmetric Dark Matter from Leptogenesis
• CP violation in scatterings, three body processes and the Boltzmann equations for leptogenesis
• Particle-antiparticle asymmetries from annihilations

Cited by in corpus (11)

• What is the $i\epsilon$ for the S-matrix?
• Cutting rules on a cylinder: a bottom-up approach to quantum kinetic theory for the early universe
• Mass-derivative relations for leptogenesis
• Mass-derivative relations and unitarity constraints for $CP$ asymmetries at finite temperature
• Modifying the Dyson Series for Unstable Particles and Resonances
• Dirac leptogenesis from asymmetry wash-in via scatterings
• Minimal effective theory for leptogenesis, dark matter, and neutrino masses
• Unitarity, real-intermediate states, and fixed-order approach to resonant dark matter annihilation
• Asymmetric dark matter from semi-annihilation: unitarity constraints and long-lived final states
• Cutting rules on a cylinder and simplified diagrammatic approach to $CP$ violation in quantum kinetic theory
• $CPT$ and unitarity constraints for higher-order $CP$ asymmetries at finite temperature